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Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
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Gadgets, Approximation, and Linear Programming
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Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Some optimal inapproximability results
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On the power of unique 2-prover 1-round games
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Computer assisted proof of optimal approximability results
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A 7/8-Approximation Algorithm for MAX 3SAT?
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Hardness of Max 3SAT with No Mixed Clauses
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Conditional hardness for approximate coloring
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A 3-Query Non-Adaptive PCP with Perfect Completeness
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SDP gaps and UGC-hardness for MAXCUTGAIN
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Balanced max 2-sat might not be the hardest
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Optimal Inapproximability Results for MAX-CUT and Other 2-Variable CSPs?
SIAM Journal on Computing
Vertex cover might be hard to approximate to within 2-ε
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Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
An optimal sdp algorithm for max-cut, and equally optimal long code tests
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Gaussian Bounds for Noise Correlation of Functions and Tight Analysis of Long Codes
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
3-bit dictator testing: 1 vs. 5/8
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Improved Inapproximability Results for Maximum k-Colorable Subgraph
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
A Hypergraph Dictatorship Test with Perfect Completeness
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Conditional Hardness of Approximating Satisfiable Max 3CSP-q
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SDP gaps for 2-to-1 and other label-cover variants
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A query efficient non-adaptive long code test with perfect completeness
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Query-efficient dictatorship testing with perfect completeness
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Query-efficient dictatorship testing with perfect completeness
Property testing
On unique games with negativeweights
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
An invariance principle for polytopes
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Approximation resistance on satisfiable instances for predicates with few accepting inputs
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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In this paper we study a fundamental open problem in the area of probabilistic checkable proofs: What is the smallest s such that NP ⊆ naPCP1,s[O(log n),3]? In the language of hardness of approximation, this problem is equivalent to determining the smallest s such that getting an s-approximation for satisfiable 3-bit constraint satisfaction problems ("3-CSPs") is NP-hard. The previous best upper bound and lower bound for s are 20/27+µ by Khot and Saket [KS06], and 5/8 (assuming NP subseteq BPP) by Zwick [Zwi98]. In this paper we close the gap assuming Khot's d-to-1 Conjecture. Formally, we prove that if Khot's d-to-1 Conjecture holds for any finite constant integer d, then NP naPCP1,5/8+ µ[O(log n),3] for any constant µ 0. Our conditional result also solves Hastad's open question [Has01] on determining the inapproximability of satisfiable Max-NTW ("Not Two") instances and confirms Zwick's conjecture [Zwi98] that the 5/8-approximation algorithm for satisfiable 3-CSPs is optimal.